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4 years ago

6

A savings account accrues interest at a rate of 3.0% yearly. If someone opens an account with $2,500, how much money would the a

ccount have after 5 years?

1 answer:

Sauron [17]4 years ago

5 0

$3\%=\frac{3}{100}=0,03\\\\
First\ year:2500+2500*0,03=2500+75=2575\\\\Second\ year:\ 2575+2575*0,03=2575+77,25=2652,25\\\\Third\ year:\ \ 2652,25+2652,25*0,03=2652,25+79,5675=\\\\2731,8175\\\\ Fourth\ year: 2731,8175+2731,8175*0,03=2731,8175+81,954525\\\\=2813,772025\\\\Fifth\ year:\ 2813,772025+2813,772025*0,03=\\\\2813,772025+84,41316075=2898,18518575\$$

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3 years ago

Find the inverse Laplace transform f(t) of the function F(s). Write uc for the Heaviside function that turns on at c, not uc(t).

zzz [600]

Answer:

F(t) $=\frac{-1}{2}e^{7(t-7)}+\frac{1}{2}e^{-7(t-7)}$

Step-by-step explanation:

We have given $F(S)=\frac{7e^{-7s}}{s^2-49}$

Now $F(S)=e^{-7s}G(s)$

Here $G(S)=\frac{7}{S^2-49}$

Now first find the Laplace inverse of G(S)

Using partial fraction

$\frac{7}{(s+7)(s-7)}=\frac{A}{(S+7)}+\frac{B}{S-7}$

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On comparing the coefficient

$A=\frac{1}{2}$ and $B=\frac{-1}{2}$

On putting the value of A and B

$G(S)=\frac{-1}{2(S+7)}+\frac{1}{2(S+7)}$

Taking inverse Laplace

$G(t)=\frac{-1}{2}e^{7t}+\frac{1}{2}e^{-7t}$

Now in G(s) there is onether term $e^{-7s}$

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3 years ago

What is the measure of the reference angle for a 112 degrees angle?

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3 years ago

You need 210 snowballs to make the perfect snow fort. you can make 15 snowballs an hour, but 2 melt every 15 minutes. how long w

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3 years ago

Solve the system by substitution.

Butoxors [25]

<u>Answer:</u>

The solution set of given equations -x-y-z = -8 and - 4x + 4y + 5z = 7 and 2x + 2z = 4 is (3, 6, -1)

<u>Solution:</u>

Given, set linear equations are

-x – y – z = -8 ⇒ x + y + z = 8 → (1)

-4x + 4y + 5z = 7 ⇒ 4x – 4y – 5z = -7 → (2)

2x + 2z = 4 ⇒ x + z = 2 → (3)

We have to solve the above given equations using substitution method.

Now take (3), x + z = 2 ⇒ x = 2 – z

So substitute x value in (1)

(1) ⇒ (2 – z) + y + z = 8 ⇒ 2 + y + z – z = 8 ⇒ y + 0 = 8 – 2 ⇒ y = 6.

Now substitute x and y values in (2)

(2) ⇒ 4(2 – z) – 4(6) – 5z = - 7 ⇒ 8 – 4z – 24 – 5z = -7 ⇒ -9z – 16 = -7 ⇒ 9z = 7 – 16 ⇒ 9z = -9 ⇒ z = -1

Now substitute z value in (3)

(3) ⇒ x – 1 = 2 ⇒ x = 2 + 1 ⇒ x = 3

Hence, the solution set of given equations is (3, 6, -1).

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3 years ago